 This was dealt with in Example 3.1(1) in [1]}, and
denoted by \(D(\lambda )\) . From the perspective of periodicity,
it has a
singular version: when the scalar parameter \(\lambda =1\)  it is not periodic.
In that case \(e_1H/S_1\cong e_2H/S_2\)  and is indecomposable, and the simple modules belong to an Auslander-Reiten component
of type \(D\) . The algebra is
of semidihedral type, part of the family \(SD(2\mathcal {B})_3\)  in [2]}
and it is a hybrid algebra (and not singular as such).
